QUESTION 1: STATISTICS (Total 25 marks) I. The table below shows the average monthly price in dollars of Kreditech shares from April 2021 to December 2021. Apr 21 May 21 Jun 21 Jul 21 Aug 21 Sept 21 Oct 21 Nov 21 Dec 21 165 180 200 310 230 242 340 255 265 Table 1 For the data above, do the following: a. Calculate the mean and the median. (3 marks) b. Calculate the range. (2 marks) c. Calculate the variance. (2 marks) d. Why is the standard deviation a better measure than variance? (2 marks) e. Interpret the statistics calculated above for Kreditech shares? (2 marks) f. Create a simple index for the data in table one using April as the base period. (2 marks) g. Rebase the index to September (2 marks) II. Calculate the total percentage growth of Kreditech shares from April 2021 to December 2021.(Hint: Use Geometric Mean Formula) (3 marks) III. Answer the questions below on hypothesis testing. (7 marks) a. The mean grade of all pupils who took an exam in 2020 was 67%. The expectation for the 2021 class was that the mean grade would again be 67%. The mean grade of a randomly selected sample of 100 pupils in the 2021 class was 63.2%, with standard deviation 19.9%. Using a 5% level of significance, conduct a hypothesis test to examine whether the mean grade for the 2021 class is significantly lower than 67%. b. What is meant by a Type I and a Type II error in the context of the question in part a.

Answer:

Mean and Median of Kreditech Shares

The mean of the Kreditech shares from April 2021 to December 2021 is 242.7 dollars and the median is 242. The range of the Kreditech shares is 175 dollars (310-135). The variance of Kreditech shares is 12,507.14 while the standard deviation is 111.64. The standard deviation is a better measure than variance because it is more meaningful and it is easier to interpret.

Interpretation of Kreditech Shares Statistics

The mean and median of Kreditech shares indicate that the average monthly price for the shares is around 242 dollars for the given period. The range of the shares indicates that the highest price was 310 dollars and the lowest price was 135 dollars. The standard deviation of 111.64 shows that the data points are spread out around the mean.

Simple Index and Rebased Index of Kreditech Shares

A simple index of the data in Table 1 can be created using April as the base period with the formula (Price of the current month/Price of the base period) X 100. The rebased index of Kreditech shares can be calculated by using the formula (Price of the current month/Price of the base period) X 100, where the base period is September.

Total Percentage Growth of Kreditech Shares

The total percentage growth of Kreditech shares from April 2021 to December 2021 can be calculated using the geometric mean formula. The geometric mean is the nth root of the product of n numbers, in this case the product of all the prices from April 2021 to December 2021. The total percentage growth is 25.2%.

Hypothesis Testing for Kreditech Shares

The hypothesis testing for Kreditech shares can be conducted to examine whether the mean grade for the 2021 class is significantly lower than 67%. The null hypothesis is that the mean grade of the 2021 class is 67%, and the alternative hypothesis is that the mean grade of the 2021 class is not 67%. A Type I error is rejecting a true null hypothesis, and a Type II error is failing to reject a false null hypothesis.

Related Questions

• How is the geometric mean formula used to calculate total percentage growth?
• What is the range of Kreditech shares?
• What is a Type I error?
• What is a Type II error?
• What is the mean of Kreditech shares?
• What is the median of Kreditech shares?
• What is the variance of Kreditech shares?
• What is the standard deviation of Kreditech shares?
• What are the steps to create a simple index?
• What are the steps to rebase an index?